research/cosmic-web/docs/.
The thermal Sunyaev–Zel’dovich effect, in one paragraph
Photons of the cosmic microwave background (CMB) crossing a pocket of hot ionised gas occasionally scatter off its free electrons and pick up a little energy — inverse Compton scattering. The distortion this imprints on the CMB spectrum is the thermal Sunyaev–Zel’dovich (tSZ) effect (Sunyaev & Zel’dovich 1972), and its amplitude at each sky position is the Compton-y parameter: the line-of-sight integral of the electron pressure,
\[y \;=\; \frac{\sigma_{\mathrm{T}}}{m_e c^{2}} \int P_e \, dl , \qquad P_e = n_e k_{\mathrm{B}} T_e ,\]with \(\sigma_{\mathrm{T}}\) the Thomson cross-section, \(m_e c^2\) the electron rest energy, \(n_e\) the electron density and \(T_e\) the electron temperature. y is dimensionless and, usefully, independent of redshift: a parcel of hot gas contributes the same y whether nearby or distant. Galaxy clusters reach y ~ 10⁻⁴–10⁻⁵; the warm–hot intergalactic medium (WHIM, gas at 10⁵–10⁷ K) sits near y ~ 10⁻⁸ for the stacked luminous-red-galaxy (LRG) pair bridges targeted here (prominent individual intercluster bridges reach 10⁻⁷–10⁻⁶) — around a hundred times below the noise per pixel of the all-sky Planck y map. tSZ is the filament probe of choice because y scales with gas density \(n_e\) to the first power, where X-ray emission scales as \(n_e^2\) and so collapses in diffuse gas. Both maps used in the series are component-separated y maps: Planck (10′ beam) and the Atacama Cosmology Telescope’s ACT DR6 (1.6′ beam), where the beam is the instrument’s angular resolution.
Stacking: seeing 10⁻⁸ in a 10⁻⁶ map
No single filament is visible, so the campaign averages the map over many sky positions selected by an external catalogue — stacking. Averaging N roughly independent positions beats the noise down by \(\sqrt{N}\), but the zero point of a y map is not trustworthy, so the measurement is always differential: the stacked value minus the same stack on control positions, with significance defined as
\[\mathrm{SNR} \;=\; \frac{\text{stack} - \langle \text{stack}_{\mathrm{ctrl}} \rangle}{\sigma_{\mathrm{ctrl}}}\]over hundreds of control realisations. Everything then hinges on whether the controls are exposed to the same systematics as the signal positions.
Controls must match the sky’s systematics
The first pass (E3) stacked spine networks extracted from 274,075 BOSS CMASS-North galaxies (18 tiles of 512 h⁻¹Mpc, spines at matched total length per method) on the Planck y map, against 200 footprint-constrained controls built by rotating in right ascension and reflecting in declination: 4.8σ (Hessian spines) and 4.1σ (orientation-lift spines). But those transformations change galactic latitude — and galactic foregrounds (dust, and the residual it leaves in a y map) vary with latitude, so signal and controls sampled different foreground exposure. The second pass (E3b) drew 200 control sets rejection-matched to the spine points’ galactic-latitude histogram in 2° bins, so no latitude-dependent foreground can contribute. The detection strengthened: 8.99σ (Hessian; per-bin SNRs can exceed the overall figure because neighbouring bins are correlated — and, with 200 empirical controls, σ’s this large are Gaussian-tail extrapolations of the measured null, not counted exceedances) and 6.86σ (lift). A stricter control does not necessarily shrink a real signal — it removes a variance term that was diluting it.
The 9σ spine detection, decomposed
At 8.99σ the extracted web demonstrably sits on hot gas — but whose gas? The survey galaxies themselves carry hot halos, so E3b masked a 7′ disc around every catalogue galaxy, identically in signal and controls. The excess collapsed to 1.95σ (Hessian) and 0.07σ (lift): the spine-stack signal is dominantly the tracers’ own halo gas, with at most a hint of a between-halos (WHIM) component. The radial profile extends to ≥60′ but cannot discriminate extended filament gas from clustered halo contributions at a 10′ beam (E3b). Two conclusions: the spine networks are physically real (they trace hot gas at high significance), and isolating filament gas needs a sharper instrument and a different estimator.
research/cosmic-web/artifacts/e3b_results.json.
The beam sets what you can see
The obvious sharper instrument, ACT DR6 at 1.6′, at first made things worse: the same spine stack dropped to 2.95σ unmasked (versus Planck’s 9σ on the overlapping footprint), and the masked residual stayed below the pre-registered 3σ gate (1.77σ at 3′ masking; E3c). The working diagnosis is a scale mismatch: the spines are projected through a ~250 h⁻¹Mpc redshift shell, so their stacked signal is coherent on degree scales, where a ground-based map is least reliable while excelling at arcminutes. (A caveat belongs here: ACT DR6’s y-map co-adds Planck information at large scales, so pure filtering cannot be the whole story — transfer-function and footprint effects on degree scales remain to be pinned down.) The lesson: an analysis design must place its signal at the angular scales its instrument preserves. E3c’s prescription — go small-scale, individual structures instead of shell projections — became the pair-bridge design.
Pair bridges: cancel the halos by symmetry
Take close galaxy pairs — transverse separation 6–14 h⁻¹Mpc, line-of-sight separation < 6 h⁻¹Mpc — which simulations expect to be connected by filament bridges. The estimator (E3d, refined in E3d-v2): average y in a 2′ disc at the pair midpoint, and subtract the mean of the same disc at ring control points at ±60°, ±90° and ±120° around each galaxy, at identical angular distance from that galaxy. Any circularly symmetric halo profile contributes exactly zero by construction — the control points sit at the same distance from the halo as the midpoint does. What survives is gas that lives preferentially on the inter-pair axis: the bridge. Over 876,639 CMASS pairs this gave 2.28×10⁻⁸ at 5.24σ on ACT and 2.97×10⁻⁸ at 19.3σ on Planck with per-pair bootstrap errors (E3d-v2).
The validity battery and the final numbers
Two upgrades of rigour (E3e; Appendix B3 discusses both as general methods). First, pairs overlap on the sky, so bootstrap over pairs is too optimistic: a jackknife over 50 right-ascension patches deflates the significances by 1.6–2.4×. Second, a physically-null control: pairs with the same transverse window but line-of-sight separation 25–40 h⁻¹Mpc — same sky geometry, no possible bridge. The nulls came back zero on ACT (1.65σ) but 4.7σ nonzero on Planck (1.80×10⁻⁸): at a 10′ beam, the second galaxy’s smeared halo contributes more at the midpoint than at the ring controls (which sit farther from it), manufacturing a fake bridge — beam leakage, now measured rather than suspected.
| control stage | ACT DR6 | Planck |
|---|---|---|
| pair bootstrap errors (E3d-v2) | 5.24σ (2.28×10⁻⁸) | 19.3σ (2.97×10⁻⁸) |
| sky-patch jackknife (E3e) | 3.30σ | 7.99σ |
| null-pair subtracted (E3e) | ≈1.6σ (1.4×10⁻⁸ ± 0.9) | ≈2.4σ (1.2×10⁻⁸ ± 0.5) |
The bottom row is the physically meaningful bridge amplitude: ~1.2–1.4×10⁻⁸, at ≈2σ per instrument, mutually consistent between two independent telescopes and matching the published luminous-red-galaxy pair-bridge measurements (~1–2×10⁻⁸; de Graaff et al. 2019, Tanimura et al. 2019). The campaign therefore reports a reproduction of the literature amplitude under honest errors and physical nulls — not an independent 5σ detection; upgrading it would need model-based two-halo subtraction and a joint-map likelihood. The recurring moral of the series holds to the last experiment: every strong claim, put under its own strictest control, shrinks to its honest core — and the honest core here still says the bridges are real.
Back to the series
Back to the series: The Geometry of the Cosmic Web: A Research Program · Two Ways to See a Cosmic Filament · From Cosmic Filaments to Curved Spacetime.
References
- R. A. Sunyaev & Ya. B. Zel'dovich (1972). "The observation of relic radiation as a test of the nature of X-ray radiation from the clusters of galaxies." Comments Astrophys. Space Phys. 4, 173.
- Planck Collaboration (2016). "Planck 2015 results. XXII. A map of the thermal Sunyaev–Zeldovich effect." A&A 594, A22.
- W. Coulton et al. (2024). "Atacama Cosmology Telescope: high-resolution component-separated maps across one third of the sky." Phys. Rev. D 109, 063530. The ACT DR6 Compton-y map.
- A. de Graaff et al. (2019). "Probing the missing baryons with the Sunyaev–Zel'dovich effect from filaments." A&A 624, A48.
- H. Tanimura et al. (2019). "A search for warm/hot gas filaments between pairs of SDSS luminous red galaxies." MNRAS 483, 223–234.
- Experiment reports E3, E3b, E3c, E3d, E3d-v2, E3e, in
research/cosmic-web/docs/of the repository.